During World War II it was exciting and unexpected for Hayek to find someone else, from Vienna, who was interested in many of the same topics that he was. The Open Society and Its Enemies has three main parts, on Plato, Hegel, and Marx. The next main chapters in Hayek's uncompleted The Abuse and Decline of Reason, on which he was at work then, were to be on Hegel and Marx. In addition, Popper's scholarly style was similar to Hayek's, with extremely extensive notes.
Hayek's Journey: The Mind of Friedrich Hayek (2003) - Ch. 15 : Karl Popper